1. Field of the Invention
The present invention relates to a transmitted wavefront measuring method using a Talbot interferometer.
2. Description of the Related Art
Previously, as one of methods of measuring a transmitted wavefront of a test optical system (a test object) having a large aberration, a measuring method using a Talbot interferometer as disclosed in APPLIED OPTICS/Vol. 23, No. 11/1984, pp 1760-1764 (reference 1) is known. According to reference 1, a Talbot condition (a condition where an interference pattern appears) is represented as the following expression (1) using a distance Zt between a diffraction grating and an image pickup element and a distance Z0 between the diffraction grating and an image point of the test optical system.
                                          (                                                            Z                  0                                ⁢                                  Z                  t                                                                              Z                  0                                -                                  Z                  t                                                      )                    ·                      (                          λ                              2                ⁢                                  d                  2                                                      )                          =        N                            (        1        )            
In the expression (1), d is a pitch (a period) of a diffraction grating, λ is a wavelength of a light source, and N is an integer. A frequency f0 of an interference pattern in this case is represented as the following expression (2).
                              f          0                =                              Z            0                                              (                                                Z                  0                                -                                  Z                  t                                            )                        ⁢            d                                              (        2        )            
When the transmitted wavefront is restored using the interference pattern, an FFT method (a Fast Fourier Transform method) is commonly used. J. Opt. Soc. Am./Vol. 72, No. 1/1982, pp 156-160 (reference 2) discloses a technology for moving a first spectrum on a spatial frequency of the interference pattern by a spatial carrier frequency to restore the transmitted wavefront of the test optical system with regard to the FFT method. Reference 1 also discloses a case where a transmitted wavefront of a test optical system can be restored by analyzing the frequency f0 defined by the expression (2) as a spatial carrier frequency in reference 2. This uses a phenomenon where an aberration of the test optical system causes a spectral broadening when the interference pattern is represented on the spatial frequency.
Commonly, position information of an interference spectrum is a tilt component of a phase distribution. In a shearing interferometer such as a Talbot interferometer, the tilt component of the phase distribution becomes a focus component of a transmitted wavefront shape. Therefore, there is also a method of ignoring the position information of the interference spectrum to obtain a transmitted wavefront where the focus component has been removed.
In the method of restoring the transmitted wavefront as described above, in order to measure the transmitted wavefront including the focus component, it is necessary to exactly recognize the distance Zt between the diffraction grating and the image pickup element and the distance Z0 between the diffraction grating and the image point of the test optical system. However, when the aberration of the test optical system is large, it is difficult to exactly determine the spatial carrier frequency f0 that is a reference in obtaining the focus component because the test optical system does not have one image point. Even if these distances Zt and Z0 can be exactly determined, it is difficult to exactly dispose an optical element of a measuring system at a designed position. Thus, in a conventional technology, when the test optical system with a large aberration is measured by using the Talbot interferometer, the focus component cannot be measured with a high degree of accuracy.